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A fixed point of a function f is a number c in its domain such that . (The function doesn’t move c; it stays fixed.)

(a) Sketch the graph of a continuous function with domain whose range also lies in. Locate a fixed point of f.

(b) Try to draw the graph of a continuous function with domain and range in that does not have a fixed point. What is the obstacle?

(c) Use the Intermediate Value Theorem to prove that any continuous function with the domain and range in must have a fixed point.

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Trinidad Tremblay
Trinidad TremblayLv2
25 May 2020

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